Global asymptotic stability of delayed neural networks with discontinuous neuron activations

Neurocomputing

Volumn 118, Issue , 2013, Pages 322-328

  Xiao, Jian ^a,b   Zeng, Zhigang ^a,b   Shen, Wenwen ^a,b  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b BEIJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

Author keywords

Asymptotic stability; Discontinuous neural networks; Fillipov solution

Indexed keywords

DELAYED NEURAL NETWORKS; EXISTENCE OF AN EQUILIBRIUM POINTS; EXISTENCE OF SOLUTIONS; GLOBAL ASYMPTOTIC STABILITY; GLOBAL ASYMPTOTICAL STABILITY; GLOBAL STABILITY; LYAPUNOV-KRASOVSKII STABILITY THEORY; SET-VALUED MAP;

ASYMPTOTIC STABILITY; LINEAR MATRIX INEQUALITIES; THEOREM PROVING;

NEURAL NETWORKS;

ANALYTICAL PARAMETERS; ARTICLE; ARTIFICIAL NEURAL NETWORK; DISCONTINUOUS NEURON ACTIVATION; LERAY SCHAUDER THEOREM; LINEAR SYSTEM; LYAPUNOV KRASOVSKII STABILITY THEORY; MATHEMATICAL PHENOMENA; PRIORITY JOURNAL; STATISTICAL ANALYSIS;

EID: 84881230684     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2013.02.021     Document Type: Article

References (33)

1. Yang Y.Q., Cao J.D. A feedback neural network for solving convex constraint optimization problems. Appl. Math. Comput. 2008, 201:340-350.
2. Kaslika E., Sivasundaramc S. Impulsive hybrid discrete-time Hopfield neural networks with delays and multistability analysis. Neural Networks 2011, 24:370-377.
3. Shen Y., Wang J. Almost sure exponential stability of recurrent neural networks with Markovian switching. IEEE Trans. Neural Networks 2009, 20:840-855.
4. Liu Y.R., Wang Z.D., Liang J.L., Liu X.H. Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays. IEEE Trans. Neural Networks 2009, 20:1102-1116.
5. Liao X.X., Luo Q., Zeng Z.G., Guo Y.X. Global exponential stability in Lagrange sense for recurrent neural networks with time delays. Nonlinear Anal. Real World Appl. 2008, 9:1535-1557.
6. Liu Z.W., Zhang H.G., Zhang Q.L. Novel stability analysis for recurrent neural networks with multiple delays via line integral-type L-K functional. IEEE Trans. Neural Networks 2010, 21:1710-1718.
7. Hong Q., Zhang Y., Wang X.B. A winner-take-all neural networks of N linear threshold neurons without self-excitatory connections. Neural Process. Lett. 2009, 29:143-145.
8. Liu Z.W., Zhang H.G., Wang Z.S. Novel stability criterions of a new fuzzy cellular neural networks with time-varying delays. Neurocomputing 2009, 72:1056-1064.
9. Wang L.L., Chen T.P. Complete stability of cellular neural networks with unbounded time-varying delays. Neural Networks 2012, 36:11-17.
10. Faydasicoka O., Arikb S. Equilibrium and stability analysis of delayed neural networks under parameter uncertainties. Appl. Math. Comput. 2012, 218:6716-6726.
11. Du B.Z., Lam D. Neural networks letter. stability analysis of static recurrent neural networks using delay-partitioning and projection. Neural Networks 2009, 22:343-347.
12. Zhang H.G., Wang Z.S., Liu D.R. Global asymptotic stability of recurrent neural networks With multiple time-varying delays. IEEE Trans. Neural Networks 2008, 19:855-873.
13. Zhang W.B., Tang Y., Fang J.A., Wue X.T. Stability of delayed neural networks with time-varying impulses. Neural Networks 2012, 36:59-63.
14. Wu A.L., Zeng Z.G. Dynamic behaviors of memristor-based recurrent neural networks with time-varying delays. Neural Networks 2012, 36:1-10.
15. Hopfield J.J. Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. 1984, 81:3088-3092.
16. Forti M., Nistri P. Global convergence of neural networks with discontinuous neuron activation. IEEE Trans. Circ. Syst. I 2003, 50:1421-1435.
17. Forti M., Nistri P., Papini D. Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Trans. Neural Networks 2005, 16:1449-1463.
18. Forti M., Grazzini M., Nistri P. Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipchitz activations. Physica D 2006, 214:88-99.
19. Forti M. M-matrices and global convergence of discontinuous neural networks. Int. J. Circuit Theory Appl. 2007, 35:105-130.
20. Allegretto W., Papini D., Forti M. Common asymptotic behavior of solutions and almost periodicity for discontinuous, delayed, and impulsive neural networks. IEEE Trans. Neural Networks 2010, 21:1110-1125.
21. Lu W.L., Chen T.P. Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions. Neural Networks 2005, 18:231-242.
22. Liu W.L., Chen T.P. Almost periodic dynamics of a class of delayed neural networks with discontinuous activations. Neural Comput. 2008, 20:1065-1090.
23. Wang J.F., Huang L.H., Guo Z.Y. Global asymptotic stability of neural networks with discontinuous activations. Neural Networks 2009, 22:931-937.
24. Qin S., Xue X.P. Global exponetial stability and global convergence in finite time of neural networks with discontinuous activations. Neural Process. Lett. 2009, 29:189-204.
25. Cai Z.W., Huang L.H., Guo Z.Y., Chen X.Y. On the periodic dynamics of a class of time-varying delayed neural networks via differential inclusions. Neural Networks 2012, 33:97-113.
26. Liu X.Y., Cao J.D. Robust state estimation for neural networks with discontinuous activations. IEEE Trans. Syst. Man Cybern. Part-B Cybern. 2010, 40:1425-1437.
27. Nie X.B., Cao J.D. Existence and global stability of equilibrium point for delayed competitive neural networks with discontinuous activation functions. Int. J. Syst. Sci. 2012, 43:459-474.
28. Zuo Y., Wang Y., Huang L., Wang Z., Liu X., Li C. Robust stability criterion for delayed neural networks with discontinuous activation functions. Neural Process. Lett. 2009, 29:29-44.
29. Aubin J.P., Frankowska H. Set-Valued Analysis 1990, Birkhauser, Boston.
30. Wang J.F., Huang L.H., Guo Z.Y. Dynamical behavior of delayed Hopfield neural networks with discontinuous activations. Appl. Math. Model. 2009, 33:1793-1802.
31. Yang Y., Cao J.D. Solving quadratic programming problems by delayed projection neural network. IEEE Trans. Neural Networks 2006, 17:1630-1634.
32. Chen L., Hou Z.G., Tan M. A neutral-type delayed projection neural network for solving nonlinear variational inequalities. IEEE Trans. Circuits Syst. II-Express Briefs 2008, 55:806-810.
33. Chen L., Hou Z.G., Tan M. A delayed projection neural network for solving linear variational inequalities. IEEE Trans. Neural Networks 2009, 20:915-924.